Non-translation-invariance and the synchronization problem in wavelet sampling

DOI10.1007/s10440-009-9480-yzbMath1175.94061OpenAlexW2025316619MaRDI QIDQ1038750

Jeffrey A. Hogan, Joseph D. Lakey

Publication date: 20 November 2009

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-009-9480-y

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sampling theory in information and communication theory (94A20)

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A sharp Balian-Low uncertainty principle for shift-invariant spaces, Principal shift-invariant spaces with extra invariance nearest to observed data, Quantifying invariance properties of shift-invariant spaces, Uncertainty principles and Balian-Low type theorems in principal shift-invariant spaces, Uncertainty principles in finitely generated shift-invariant spaces with additional invariance, Maximal discrepancy for multiply generated shift-invariant spaces, Frame properties of shifts of prolate spheroidal wave functions

Cites Work

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• Translation invariance of orthogonal multiresolution analyses of \(L^2(\mathbf R)\)
• Time-frequency and time-scale methods. Adaptive decompositions, uncertainty principles, and sampling
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• Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
• Ten Lectures on Wavelets
• Continuous and Discrete Wavelet Transforms
• The Zak transform and sampling theorems for wavelet subspaces
• On sampling theorem, wavelets, and wavelet transforms
• SAMPLING AND OVERSAMPLING IN SHIFT-INVARIANT AND MULTIRESOLUTION SPACES I: VALIDATION OF SAMPLING SCHEMES
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